Question

Which of the following best describes the

graph of the system of equations shown
below?
6x − 14y = −28
3y − 7x = −14
A The lines are parallel.
B The lines are the same.
C The lines intersect but are not
perpendicular.
D The lines intersect and are perpendicular.

Answer 1

First, you want to find out what the slope and the y-intercept is, you must put both equations in y=mx+b from.

6x − 14y = −28 :First, subtract the 6x over to the right
-6x -6x

(-14y = -6x - 28) ÷ -14 :Then, divide the whole equation by -14

y = 6/14x + 2 :Now, reduce the fraction, divide both the top and the bottom by 2

y = 3/7x + 2

3y − 7x = −14 :First, add the 7x over to the right side
+7x +7x

(3y = 7x - 14) ÷ 3 :Next, divide the whole equation by 3

y = 7/3x - 14/3


y = 3/7x + 2 slope: 3/7 y-int.: 2

y = 7/3x - 14/3 slope: 7/3 y-int.: -14/3 or -4 7/10 or -4.7

C. Your answer is C. They will eventually intersect, but not at a right angle.

Answer 2

`k:6x-14y=-28\ \ \ \ |subtract\ 6x\ from\ both\ sides\\\\-14y=-6x-28\ \ \ \ \ \ |divide\ both\ sides\ by\ (-14)\\\\y=(-6)/(-14)x-(28)/(-14)\\\\y=(3)/(7)x+2\\----------------------------\\l:3y-7x=-14\ \ \ \ \ |add\ 7x\ to\ both\ sides\\\\3y=7x-14\ \ \ \ \ \ |divide\ both\ sides\ by\ 3\\\\y=(7)/(3)x-(14)/(3)`


`Two\ lines\ are\ perpendicular\ if\ product\ of\ the\ slopes\ is\ equal\ -1.\\\\k:y=(3)/(7)x+2\to the\ skolpe\ m_k=(3)/(7)\\\\l:y=(7)/(3)x-(14)/(3)\to the\ slope\ m_l=(7)/(3)\\\\m_k* m_l=(3)/(7)*(7)/(3)=1\\eq-1\\\\conclusion:the\ lines\ are\ not\ perpendicular\\\\Two\ lines\ are\ parallel\ if\ the\ slopes\ are\ equal.\\\\m_k=(3)/(7);\ m_l=(7)/(3)\to m_k\\eq m_l\\\\conclusion:the\ lines\ are\ not\ parallel`



`Answer:\boxed{C-The\ lines\ intersect\ but\ are\ not\ perpendicular.}`